I think the Republic is dead at this point, if its survival is the point of this POD. Once your past the Sulla-Marian wars (heck post-Grachhi) its basically rearranging deck chairs on the Titanic.
Even the First Triumverate was probably screwed. Pompey doesn't really want to lose power, and he doesn't want to lose his (in his eyes) senior position in the relationship with Caesar. Basically, Caesar ambitions and Pompey's sense of entitlement are going to conflict regardless of the marital alliances. In the Second Triumverate Octavia's marriage to Antony wasn't enough to keep Octavian and Antony from war. I think the same applies here. Combine a Pompey wary of Caesar and the Optimates looking for a way to bring down the Triumverate and you've got a conflict.